‘I EXTEND to you and the Afghan people my sincere apologies.’’ President Obama sent this message to Afghan President Hamid Karzai last week, in the thick of mass protests after US personnel burned copies of the Koran. NATO commander General John R. Allen had earlier offered “sincere apologies . . . to the noble people of Afghanistan,’’ but the demonstrations raged on. Members of Afghanistan’s parliament called for jihad against Western forces, at least two coalition soldiers were shot dead, and multiple civilians were killed in the violence that accompanied the protests.

Book burning can universally spark visceral reactions, especially when holy texts are denigrated, but the reactions of Afghan mobs across the country can strike Westerner observers as over the top, especially when the disrespect shown the Koran in this case seems to have been, as President Obama said, “inadvertent.’’ But in a way, that makes the insult worse. Muslims in Afghanistan can ask: After a decade in our midst, do you really understand so little?

The Koran is not just another holy book, analogous to the Bible. Religions differ from one another, and comparisons can be deceiving, but my understanding as an outsider is that the Koran stands in Islam less as the Bible stands in Christianity than as Jesus does. The recited Koran, that is, invokes the “real presence’’ of God. The book is not divine in itself, but it makes the divine available. (That the calligraphy in which the Arabic words of the Koran are rendered was itself taken to be sacred is one reason the Muslim world was slow to embrace the movable-type printing press - a hesitation that had broad cultural consequences.) If a comparison is to be made, the Koran should be handled with the reverence with which, for example, Catholics handle the consecrated host at Mass. The enraged reaction of Muslims may point less to their irrational zealotry than to the depth of Western ignorance about Islamic belief and practice.

And by the way, how well are the larger frustrations of the Afghan people understood? After a decade of war, the economy is in shambles, and security is lost. Most civilian casualties are caused by the Taliban, but coalition forces are widely taken to be invaders, not protectors. And when Predator drones, say, strike a village, the nation takes the blow. Two years ago, after 23 civilians were killed by a drone, it was General Stanley McChrystal who shaped an apology around the word “inadvertent.’’ Last month, statements of American remorse were prompted by videos showing US Marines urinating on the corpses of Taliban fighters. A week before the Koran burning, General Allen apologized for an airstrike that killed seven children. Such NATO apologies, in chorus with Karzai condemnations that require them, have become a routine mark of the coalition’s presence. “They burn our Koran, and then they apologize,’’ a demonstrator said last week. “You can’t just disrespect our holy book and kill our innocent children and make a small apology.’’

President Obama’s apology was not small. Neither was Allen’s. The general’s characterization of the Afghan people as “noble’’ struck an important note. But it is understandable why these expressions land with little weight. Last week’s outburst may, in fact, be a moment of revelation. The situation on the ground, including a shocking level of Afghan disenchantment, may finally have overtaken all American intentions and trumped all coalition plans. Obama had already been accelerating the end of the NATO war in Afghanistan. Mass protests against the coalition can only reinforce that purpose.

What is new here is the way in which a stubborn ignorance of basic Islamic sensibilities has been paired with a failure to grasp the real character of the experience the Afghan nation has undergone during the decade since our arrival. Whatever motives drove the American war in the beginning, and however unrealistic American expectations of the Kabul government may have been, the one undeniable result of the US intervention is the profound alienation of a people we claimed to want to help. They have taken to the streets in droves, and their fists are shaking at us. Perhaps now as we Americans offer our apologies, we see as well as anyone how for short they must fall.

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